From the point of view of noncommutative geometry, the supergeometry is a very mild special case of noncommutativity in geometry: some coordinates commute, some anticommute.
For more see at geometry of physics -- supergeometry.
Some historically influential general considerations are in
Introductory lecture notes include
L. Caston, R. Fioresi, Mathematical Foundations of Supersymmetry (arXiv:0710.5742)
Alexander Voronov, Maps of supermanifolds , Teoret. Mat. Fiz. (1984) Volume 60, Number 1, Pages 43–48
A summary/review is in the appendix of
Anatoly Konechny and Albert Schwarz,
On -dimensional supermanifolds in Supersymmetry and Quantum Field Theory (D. Volkov memorial volume) Springer-Verlag, 1998 , Lecture Notes in Physics, 509 , J. Wess and V. Akulov (editors)(arXiv:hep-th/9706003)
Theory of -dimensional supermanifolds Sel. math., New ser. 6 (2000) 471 - 486
Formulation in terms of synthetic differential supergeometry is in
For many more references see at supermanifold.
especially in the contribution
The appendix there
means to sort out various sign conventions of relevance.
For more on this see at superalgebra.
this is a chapter in
P. Deligne, P. Etingof, D.S. Freed, L. Jeffrey, D. Kazhdan, J. Morgan, D.R. Morrison, E. Witten (eds.) Quantum Fields and Strings, A course for mathematicians, 2 vols. Amer. Math. Soc. Providence 1999. (web version)
Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily, chapter 3 of Advanced classical field theory, World Scientific (2009)
Gennadi Sardanashvily, Noether’s Theorems: Applications in Mechanics and Field Theory, Studies in Variational Geometry, 2016